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Consider a string of mass per unit length µ and charge per unit length η, held at tension Tand oriented in the x-direction. The string is free to vibrate in both the y- and z-directions. 5A: Argue that small displacements y(x, t) and z(x, t) describing the motions of the string in the two transverse directions obey ∂2y/∂t2 = v^2 (∂2y/∂x2)........ eqn a ∂2z/∂t2 = v^2 (∂2z/∂x2)........ eqn b for an appropriate wave velocity v which you should find. 5B: Now suppose we turn on a magnetic field B = B0xˆ. 5B.1. How do the wave equations above get modified? 5B.2. Define the variables w± = y ± iz. Show that w±(x, t) obey decoupled differential equations (i.e. you get one equation for w+ and one for w−).

Consider a string of mass per unit length µ and charge per unit length η, held at tension Tand oriented in the x-direction. The string is free to vibrate in both the y- and z-directions. 5A: Argue that small displacements y(x, t) and z(x, t) describing the motions of the string in the two transverse directions obey ∂2y/∂t2 = v^2 (∂2y/∂x2)........ eqn a ∂2z/∂t2 = v^2 (∂2z/∂x2)........ eqn b for an appropriate wave velocity v which you should find. 5B: Now suppose we turn on a magnetic field B = B0xˆ. 5B.1. How do the wave equations above get modified? 5B.2. Define the variables w± = y ± iz. Show that w±(x, t) obey decoupled differential equations (i.e. you get one equation for w+ and one for w−).

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Consider a string of mass per unit length µ and charge per unit length η, held at tension Tand oriented in the x-direction. The string is free to vibrate in both the y- and z-directions.
 5A: Argue that small displacements y(x, t) and z(x, t) describing the motions of the string in the two transverse directions obey
∂2y/∂t2 = v^2 (∂2y/∂x2)........ eqn a
∂2z/∂t2 = v^2 (∂2z/∂x2)........ eqn b
for an appropriate wave velocity v which you should find.

 5B: Now suppose we turn on a magnetic field B = B0xˆ.

5B.1. How do the wave equations above get modified?

5B.2. Define the variables
w± = y ± iz.
Show that w±(x, t) obey decoupled differential equations (i.e. you get one equation for w+ and
one for w−).

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